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<title>
    T-MATS: Help for 0-D Transient Conduction Library Block
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    <h1>
      T-MATS:  0-D Transient Conduction Library Block
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<div class="purpose">
        Purpose
</div>

<p>
    This block can be used to model the transient conduction of a lumped system via
    the lumped capacitance method.
</p>

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<div class="background">
        Background
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<p>
    To compute the final temperature, this block utilizes the following equation:

    $$T_f = (T_i - T_{inf})*\textit{e}^\frac{\textit{L_M*c_M*rho_M}}{\textit{h_M*dt_M}} + T_{inf} $$

    The specifics of each variable in the above equation are detailed in the tables below.

<p>
The export values are calculated based on a single time step. If additional
dynamic behavior is required a simulink memory block may be used to update the
temperature initial conditions.

<p>
Additionally, the system checks that the input numbers will result in a feasible result based on a
generally accepted Biot number (<i>Bi</i>) limitiation.
$$Bi =\frac{\textit{h_M*L_M}}{\textit{k_M}}\leq 0.1$$
This limitation allows for the assumption that
temperature variation within the body of the lumped sum is negligible.
An error message will appear if the input parameters are not appropriate for the model
being used by this block.

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<div class="instructions">
        Instructions
</div>

<p>
    To use this block:
    <ul>
        <li> Connect the initial temperature and out-of-system temperature values to the corresponding places on the block.
        <li> Connect the output temperature to the next block in your simulation.
        <li> Double click the block and specify the time step, convection heat transfer coefficient, thermal conductivity constant, density, specific heat, and the characteristic length.
    </ul>
</p>

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<div class="inputs">
         0-D Transient Conduction Inputs
</div>

<table>
    <tr><th> Input </th><th >Description</th></tr>
    <tr><td>Tinf</td><td>Out of Lumped System Temperature</td></tr>
    <tr><td>Ti</td><td>Initial Lumped System Temperature</td></tr>
</table>

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<div class="outputs">
         0-D Transient Conduction Outputs
</div>

<table>
    <tr><th> Output </th><th> Description </th></tr>
    <tr><td>Tf</td><td>Final Lumped System Temperature</td></tr>
</table>

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<div class="maskvars">
         0-D Transient Conduction Mask Variables
</div>

<table>
    <tr><th> Mask Variable </th><th> Description </th></tr>
    <tr><td>dt_M</td><td>Time Step (dt)</td></tr>
    <tr><td>h_M</td><td>Material Convection Heat Transfer Coefficient</td></tr>
    <tr><td>k_M</td><td>Material Thermal Conductivity (k)</td></tr>
    <tr><td>rho_M</td><td>Material Density (rho)</td></tr>
    <tr><td>c_M</td><td>Material Specific Heat (C)</td></tr>
    <tr><td>L_M</td><td>System Characteristic Length (Length_c = Volume/Area)</td></tr>
</table>

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<div class = "errors">
    Potential Errors
</div>
<p>
When using this block, you may receive one of the following errors/warnings. The table
below lists the errors/warnings that you may see and the reason why it is being displayed.
</p>
<table>
    <tr><th> Error/Warning </th><th>Description</th></tr>
    <tr><td>Error in block</td><td>The input values are not appropriate for
                            using the lumped capacitance method based on a Biot number limitation.</td></tr>
</table>

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